In true experiments in which sample material can be randomly assigned to treatment conditions, most researchers presume that the condition of equal sample sizes is statistically desirable. When one or more a priori contrasts can be identified which represent a few overriding experimental concerns, however, allocating sample material unequally will…

Two bootstrapping or resampling strategies were investigated to determine their applicability to estimating standard errors and ensuing confidence intervals on variance components in two-factor random analysis of variance models. In light of prior negative findings regarding the application of bootstrapping to this particular problem, a…

Occasionally, situations arise where mixtures of two binomials with one known success parameter are met. An example in educational testing is the mastery or random guessing model in which an examinee is supposed either to master the items or not to master them and to guess blindly. This paper gives moment estimators for such mixtures and presents…

This paper evaluates the magnitude of the total error in estimates of the difference between an examinee's domain score and the cutoff score. An observed score based on a random sample of items from the domain, and an estimated cutoff score derived from a judgmental standard setting procedure are assumed. The work of Brennan and Lockwood (1980) is…

Upon learning that a form of the Sequential Tests of Educational Progress was incorrectly distributed to an unidentified number of high school students along with an answer sheet pregridded with an alternate test form, the Austin Independent School District performed the following research analyses: (1) scored the tests using the key for each…

The traditional reliability coefficient and standard error of measurement are not adequate measures of reliability for tests used to make pass/fail decisions. Answering the important reliability questions requires estimation of the joint distribution of true and observed scores. Lord's "Method 20" estimates this distribution without the…

Describes a simplified method for converting raw scores to standard scores and transforming them to "T-scores" for easy comparison of performance. Obtaining letter grades from T-scores is discussed. A reading list is included. (GH)

The National Assessment of Educational Progress in-school sampling design is a three-stage stratified design. Stratification variables include region, size of community and socioeconomic status. The three levels of sample selection are Primary Sampling Units (PSUs), schools and students. In general, two and sometimes three PSUs are selected from…

Comparisons of corresponding values of phi and kappa coefficients were made for 270 instances of data generated by a Monte Carlo technique to simulate a test-retest situation. Data were generated for distributions with the same mean but three different levels of standard deviation, standard error of measurement and cutting score. Ten samples of…

One aim of criterion-referenced testing is to classify an examinee without reference to a norm group; therefore, any statements about the dependability of such classification ought to be group-independent also. A population-independent index is proposed in terms of the probability of incorrect classification near the cutoff true score. The…

Because it is difficult to ascertain the dimensionality of a test composed of binary items through the use of factor analysis alone, a method is proposed that combines item characteristic curve (ICC) theory with factor analysis. Factor structure of tetrachoric correlations is distorted by non-normal distribution of ability. Item characteristics…

The mathematical derivation of the statistics used for inference in some linear models assumes that the values of the independent variables are measured without error. This assumption is often disregarded when these models are utilized in research. This study is an investigation of the consequences of the violation of this assumption for one…

Besides the ubiquitous Pearson product-moment r, there are a number of other measures of relationship that are attenuated by errors of measurement and for which the relationship between true measures can be estimated. Among these are the correlation ratio (eta squared), Kelley's unbiased correlation ratio (epsilon squared), Hays' omega squared,…

The Werts-Linn procedure for dealing with categorical errors of measurement in "Comments on Boyle's 'Path Analysis and Ordinal Data'" in The American Journal of Sociology, volume 76, number 6, May 1971, is shown to be inappropriate to the problem of ordered categories. (For related document, see TM 002 301.) (DB)

Statistics are an essential tool for making proper judgement decisions. It is concerned with probability distribution models, testing of hypotheses, significance tests and other means of determining the correctness of deductions and the most likely outcome of decisions. Measures of central tendency include the mean, median and mode. A second…